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# The area of sector JLK is `3pi ` in.`^2` . Find the measure of arc JK.

novjb | Salutatorian

Posted September 11, 2013 at 8:28 PM via web

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The area of sector JLK is `3pi ` in.`^2` . Find the measure of arc JK.

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Tagged with geometry, math

baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted September 11, 2013 at 8:38 PM (Answer #1)

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Area of the entire circle `A=pir^2`  is `36pi.`

Since the area of the sector is `3pi`  , then this represents `(3pi)/(36pi)`  or `1/12.`

Therefore this arc represents `1/12`  of the entire circle of 360 degrees.

So, this means `1/12* 360 = 30.`

Therefore arc JK = 30 degrees.` `

flbyrne | (Level 3) Assistant Educator

Posted September 11, 2013 at 10:13 PM (Answer #2)

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Determine the length of arc JK as `1/12` of the whole circumference:

Circumference=`2pi(6 `in.`)=12pi`in.

Length of arc JK`=1/12 (12pi)` in.` ``=pi` in.

Therefore the length of arc JK is 3.1416 in.

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